TIIE CORRECT AND EFFICIENT IMI)LI~',MI,N.\[A" '~ TION OF' APPI\[()PRIATENESS 
SPECIFI(:ATIONS FOR TYPF;D FlgATURI" STRUCTUR\]~,S 
Dale GeMemalm and Paul John I(ing* 
Seminar t'iir Sprachwissenschaft, Uniw',rsitS~t Tiibingen t 
ABSTRACT 
in this pa,per, we argue tha, t type inferenc- 
ing incorrectly implements a.pl)rolwiate- 
ness specifica.tions for typed \[ea.ture struc- 
tures, promote a combina.tion of l;ype res- 
olution and unfilling a,s a. correct a.nd ef'~ 
ticient Mternative, and consider the ex- 
pressive limits of this a.lterna.tive approa.ch. 
!\['hroughout, we use feature cooccurence 
restrictions as illustration and linguistic 
motivation. 
1 INTRODUCTION 
Unification lbrmMisms ma.y be either un- 
typed (DCC~s, PATR-II, 1,F(;) or typed 
(npsG). A m~L,ior reason for adding types 
to ~ forma,lism is to express restrictions 
on fea.ture cooccurences a.s in (;l's(:: \[5\] 
in order to rule out nonexista.nt tyl)es 
of objects. For example, there a.re no 
verbs which have the \[km.ture +R. The 
simplest way to express such restrictions 
is by mea.ns of a.n a.ppropria.teness pa.r- 
tim flmction Approp: Type × Feat ~ Type. 
With such a.n a.pl)rol)riatleness specifica.- 
tion lrla.tly Sllch restrictioi,s may be ex- 
pressed, though no restrictions involving 
reentrancies ma.y be expressed. 
In this pal)er, we will first in §2 survey 
the range of type eonstra.ints tha.t ma.y be 
expressed with just a. type hiera.rchy and 
*'\]'he resea.rch pl'eS(!lllL('d ill |,his; paper was pay 
tia.lly sponsored hy '\[kfilprojekt B4 "(;onsl.rahH.s on 
Grammar fl~r Efficient Ck:neration" of the Soi,der 
forschungsbereich 340 of the Deutsche \["orschungs- 
gemeinscha, ft. "VVe would also like to thank 'l'hilo 
GStz for helph,l comments ou thc ideas present.ed 
here. All mistakes a.rc of collrsc our OWll. 
IKI. Wilhehnstr. 113, |)-721174Tfilfi,,ge,, (ler- 
ma.ny, {rig,King} g'~sfs.n phil.uni-I uebingen.de. 
a.n N)propria.teness specification. Then in 
~3, we discuss how such type cons|fronts 
linty be mainta.ined under unification as 
exemplilied in the na.tura.1 language D~rs- 
ing/generation system '.l'ro\]l \[7\]. 1 Unlike 
previous systems such as ALl,:, Troll does 
not employ a.ny type infereneing, inste~M, 
a, limited amount of named disjunction 
(\[1 1\], \[12\], \[6\])is introduced to record type 
resol u tion possibilities. The a.lnount of dis- 
junction is a.lso kept small by the technique 
of unlilli,g described in \[9\]. This strategy 
a.ctua.lly ma.inta.ins apl)ropri~tteness condi- 
tions in some ca.ses in which a. type in- 
ferencing stra.tegy would fa.il, l)'inMly, in 
§4, we discuss the possibilities for gener- 
a lizillg this a.pl)roa.ch to ha.ndle a bro~Mer 
r~tnge of constra.ints, including constraints 
inw)lving reentran cies. 
2 APPROPRIATENESS 
FOR, MALISMS 
As discussed iu Gerdemann ,~ King \[8\], 
one ca.n view a.pl}rol)ria.teness CO\[lditions as 
(lelining GPSG style fea,1;tl re cooccurence re- 
strict:ions (FCRs). In \[8\], we divided FCRs 
into co,j,,ctive and di.q,,~ctive ct~sses. A 
conjunctive FCI/. is a constra.int of the fol- 
lowing fornl : 
i\[' a.n object is of ;~ cert;fin kind 
then ill deserves certa.in fea.tures 
with wdues of cert~till kinds 
An FCI~ stat:ing tha,2: a. verb must h~we v 
and N t'eatures with values A- and - re- 
spectively is a.ll example of a. conjunctive 
FCI{. A disjunctive I"CI{. is of the form: 
l rl'he "\]'roll ,qysl.em was implemented in Quintus 
Prolog by Dale (lerdemann and '\['hilo (\]Stz. 
950 
if an object is of a. cel'taiu kiud 
then it deserves cerl;a.in \[ca,1;tll'C~s 
with vMues of certa.hi kinds, 
or it deserves cerl.ahi (pei'ha.liS 
other) fea.1;u res \vil, h viiiues of 
terra.in (perlla.ps other) kinds, 
or ... 
(31: it i:leserw.;s i:erl;a.in (lmrhal)S 
other) fea,1;llres wil.h Vi, l.\[ll(~S o\[ 
certain (perha.ps other) khi,<ls 
I lo:: exa~\]nple, the following F(',|/. sl.a.t.iug 
tha,t inverCed verbs lilt|S1, lie a.uxili;tries is 
disjunctive: a verb Ilitisl; ha.re the \['(~il.l.tll'(~s 
INV and AUX with va.l/ies d a.Iid I, - a.iitl 
i L-, or - ;Mid - respectivel.y. 
Both o| these |el'illS or l,'(',lls iiHly I)(! 
expressed in a. foi'llla.iiSlli euiployhi<~ fiiiil.e 
lia,rtia.\[ order (Type, E) o| types tllldel' sub- 
8illnptioli> a, finite sel. Feat of ro;./.t;tll.(~s, 
and an a.pprol)ria.teness parl, ial rliilcl.ion 
Approp:Type X Feat -~ Type. \[uluitively; 
the l, ypes fornla.lize I;lie notion ol" kinds +,j" 
objecl, t g: t,' ill' ca.oh oil|eel, of tyl>e t' i~<i 
Mso of l;Ylle L, il, ll(\] Approp(l, f) = l I ill' (!;i('\[I 
object oF type t deserves \[eaA.urt~ f wil.\]i :i. 
Vi./.\]lle or type ft. ~@'e call S/IC\]I it. \[Ol'tll;li- 
iSlll i-i, ii ;I,\])l)l"Opl'\]al, olio,~/ fOl'lllil\]i~;lll. (',iLl'- 
peliLel",s AI,F, and (,erdeliia. i ;ill(| (i(~t,z's 
Troll are ex:-t.niples o| illilllenienl.a.Lions o| 
a,pF, ro\]) ria, Loliess |or illa.\[iSlil,s. 
l low an a.i)ln'oprhi.teness \[orniaJisnl en- 
co<les a conjunctive I:(',R is ob\.'i<>us~ bll(. 
llOW it encodes a disjuiictive I"(',1{ is less 
so. Ali exa.niple i|\]usl;ral;es best how it. is 
done. ~Ul)pOS0 that F( ',1{ \[i sl.al.es l.hal, ob- 
.iecls (if type t deserw! \[(!a.\[./ll'(!S f 'and .q, 
I)oth with boolea.I/ wdues a.ll(I \['lll'l,\[lel'lllOF(~ 
that the va.hies of f aild g iil/lSl al~r(!e, \[> 
is the disjunct\]w! I"(111. 
if a,u object is o\[ type l 
then it deserw:s f with va.lue -I- 
and q with wdue +, 
or it deserw.~s f with va.lue - 
a.nd 9 with value - 
To 0ncode \[3> first iul,rodLiCe sul/l.yltes , t ~ 
## ;+l.ll(\[ l" of I (1 E I/, 1. ), O11(! SUl)tyl)e \['()l' 
ea,ch disjuuct iu the cousequenl, of'p. Then 
encode the \]'ea.tli\['e/wthl~.~ <'on(!il.illliS in l, he 
\[irst disjunct ILy putthlg Approp(t', ./) :: ~- 
a,nd Approp(//~ q) - +, and encode the I'ea- 
ture/value conditions in the second dis- 
juu(:t by putting Approp(t',f) = -. and 
Approp(t',g) = . .'2 
This a pproa,ch Ina, kes two inll)ort;a, lll, 
closed-world type assumptious a, bouL (.he 
types tli~d; Slll)SlllIle 11o ogher types (hellCe- 
forth species), l:irst, the p;i.rtition condi- 
tiOII states tha.t for each type t, if a.n ob- 
ject is (31' type t theu the object is of ex- 
ax-I.ly o11(2 species subsulned by t. Second, 
the all-or-nothing cclndition sta, tes that 1'(31' 
each species ,q a.itd fea.ture f, either every 
el" IIO ol>,iecl, or species s deserves feature 
.#c.3 All a.l)ltroltriM,eliess \[orli+ia.lisill sllc\]l a.s 
ALl:, (\[2\], \[3\])ti,;t.l. does not uieet both c.ou- 
ditions llla.y llOt; \]lroper\[y el|cOde a, disjull('- 
five l"(:l/. For exalnple, consider disjunc- 
tive I"CI{. p. An a.I)prl;)pria.l, elleSS \[ornia.l-- 
iSlli I/lily l/O( properly encode 1,hi~t t / a.lld t" 
i'el)rt,selil, MI a.lid oilly the disjuncl, s ill the 
COll.qeqll(Hlt or \[i wiLhout the i)a.rl,ition COll- 
d\]tion. <till a.llln'ol)riill.eness \[orlila.liSlll llia,y 
IIOl. llrOl)erly encode the \[t~ii.l.llle/vii.hle (:(lll- 
<liiriOii: deinanded liy em'h disjuncl, hi the 
COli.~t!qllelil. o| p wilhoul, the a.i\[-Ol'-liot;hilig 
c(m(til.ion. 
As indicat.ed a.bove, AI, I.; is iLIi exa.tlli)le 
o| it. f(n'liialiSlU I.ha.l, does it(it ineel; llol;h o| 
1.hese closed world aS,glllnlil,iOli.g. In AI+E :-/. 
\['eli.l.tlr(~ st.i'llCtlile i.<4 won typed ifl' for ea.ch 
arc iit the te:+d.ure sI.l'tlCl;tlr0, if' 1,he SOtll'('(~ 
node is labelled wil.h type /., the targel; 
node is lallelled with 1;ype l / a.lld the il.i'c is 
IMlelled with \[ea.tlll'(~ f 1,lien Approp(/.> .f) \[ 
l/. Furl.her|note> a \['eal, urt~ strut(tire is 
>l'lds exanll)h: I:(JR is, for eXlmsil.ory l)nrl)oses, 
quilt simph'. "l'hc prolileni o\[ c.xpr('.sshig F(Jl/'s, 
however, is a l'Cal Iiuguisl.ic i)rol)lcin. As noted I)y 
Copcstakc. ct al. \[4\], it. was inipossihlc I.o c.xpress 
CV('II Ihc .~ilii\[)\]oM. forilis o\[ l"(JRs in l.hc.ii7 c×tciidcd 
VCISiOII (it' AI.E. 
'\['hc basic principle of expressing l"Clls also ex 
lends Io I"(',\[(s iuvolviug longer palhs. For exam- 
ple, to (:llSllt't: thai. for the type l, I.he path (fg) 
lakes a vahie subsuuied I)y .% one nlust tirst hll, ro 
ducc the chaiu Approp(/, f) = .,, Approp('a, g) = .~. 
Silch ilil.crlllCdialc I.'~'l)lts COllid ll(! hll.rodllced a.<-; 
part o\[ a (onilli\[al.iou sl.age.. 
4 Nob: I.hal. Ihesc cl,>s<,d world assulnplions art' 
explicitly made in Pollard ,t,. Sag (rorthcoming) 
\[14\]. 
957 
well-typable iff the feature structure sub- 
sumes a well-typed feature structure, in 
ALl.:, type infereneing is employed to en- 
sure that all feature structures are well- 
typable--in fact, all feature structures are 
well typed. Unfortunately, well-typability 
is not sufficient to ensure that disjunctive 
FCRs are satisfied. Consider, For exam- 
pie, our encoding of the disjunctive FCR p 
and suppose that 99 is the fe, ature structure 
t\[f : +,9 : -\]. 90 is well-typed, and hence 
trivially well-typable. Unfortunately, 99 vb 
elates the encoded disjunctive FCR p. The 
only way one could interpret ~ as well- 
formed 
By contrast, the Troll system described 
in this paper has an etfeetive algorithm f<>r 
deciding well-formedness, which is based 
on the idea of efficiently representing dis- 
junctive possibilities within the feature 
struetu.re. Call a well-typed feature struc- 
ture in which all nodes are labelled with 
species a resolved feature structure and 
call a set of resolved feature structures that 
have the same underlying graph (that is, 
they differ only in their node labellings) 
a disjunctive resolved feature structure. 
We write fS, ~vf8 and 'D~.)c$ for the 
collections of feature structures, resolved 
feature structures and disjunctive resolved 
feature structures respectively. Say that 
F' 6 "l~f$ is a resolvaat of F C f,"? ill' 
F and .F' have the same underlying graph 
and F subsumes 1 ''l. Let taype resolution be 
the total flmction ~: f5" --+ DgfS such 
that 7~(1,') is the set of all resolvants of l i'. 
Guided by the llartition and all-or- 
nothing coMitions, King \[13\] has fOl'inti- 
lated a semantics of feature structures and 
developed a notion of a satisfiable feature 
structure such that l'7 C .T$ is satisfial~le 
if\[' 7~(F) 7 ~ (7). C, erdemann ,% King \[8\] have 
also shown that a feature strtlcture l\]leets 
all encoded FCRs ifl" the feature structure 
is satisfiable. The Troll system, which is 
based on this idea, effectively inqflements 
type resolution. 
Why does type resohttion succeed where. 
type inferencing fails? Consider again the 
encoding of p and the feature structure 
9~. Loosely speaking, the appropriate- 
ness sl)eeifieations for type t encode the 
part of p that sta, tes that an object of 
tyl)e t deserves features f and g, both 
with boolean vahles. However, the ap- 
propriateness specifications for the speci- 
ate sul)types t' and t" of type t encode 
the part of p that states that these val- 
lies lnust agree. Well-typability only con- 
siders species if forced to. In the case 
of ~, well-typability can be estahlished 
by consklering type t alone, without the 
l)artition condition forcing one to find a 
well-typed species subsumed hy t. Conse- 
quently, well-tyl)ahility overlooks the part 
offl exehisively encoded by the ai)propri- 
ateness specifications for t' and t". Type 
resolution, on the other hand, always con- 
siders species. Thus, type resolving 9o 
cannot overlook the part of p exclusively 
encoded by tile appropriateness specifica- 
tions for t' and t'. 
3 MAINTAINING 
APPROPRIATENES S 
CONDITIONS 
l\[ow may these D~.TS be used ill an inl- 
plenmntation? A very important prop- 
erty of the class of "DT~fS is that they 
are closed under unification, i.e., if/" and 
F' 6 D~f8 then F U F' 6 D'PvfS. 4 
Given this prol)erty , it would in princi- 
ple lie possible to list the disjunctive re- 
solved feature sl;ructures h/ an iinplemen- 
tal;ion withonl; any additional type infer- 
01\]¢hig proc0dnre to ma.hltahi satisfialfil- 
ity. It would, of course~ tier be very of\[i- 
cieut 1.o work with such large disjunctions 
of featiil'e strtlctilres. These disjunetiorls 
of fea.ture structnres, however, have a sin- 
gular l)rol)erty: all of the disjuncts have 
the same shape. The disjuncts differ only 
in the types labeling i;he nodes. This prop- 
4In fa.ct., it ~:~rl~ I)~ SI~OW ~ that if t" a.nd 1'" 6 
fS then "R ( F) tJ 1"(1"') = "R ( F tO F'). Uni/ication 
of sets of fca.ture structures is defined here ill the 
standard way: S t2 ,S" = {1"\[ I"' 6 S and l"" G S" 
and 1" = 1"' H 1""}. 
958 
(!rty a.llows a. disjultctivo fesolv(,d featur(, 
structti re to I)e r(;l)rosetd,(~d more et\[icieutly 
a,s ~t sitlgle untyl)(~d l'eatur(' st.l'll(:l.llfe plus 
a, sel; of d(;pondlmt node la.h(~liugs, which 
ca.n be further (;oml)a,(:t(~d using mi, Nie(l dis. 
junction a.s in (',(~rdemann \[(i\], I)i'~\['re t(: 
Fo\]' exanH)le , SUl)l)OS(~ \v(~ I,,yl)(~ r(~solvc 
the \[ea, l, urc st, ructure t\[,f ; bool,fl; bool\] us- 
ing our encoding of p. ()he can (rosily see 
tha.t this fea.tur(~ strut:fur(, has only two I'e 
solwl, nts, which ca, n I)e colla.ps(~d iuto one 
fea,1;ure strlll:ttlro with llallV2d d\]sjunci.ion 
a,s shown below: 
II'll;1} \["'"' \] f:k , : :> f: (I t -) 0:t- LU: J ,u: (I t ) 
We now ha,vo a, \[;(mSolml)ly COml)a(:l l'q)- 
resentaJ;ion hi which t.ho l"(il{, ha.s lie(Hi 
tl';tllsl;I,t(~(\[ iul,o a. Ila, ill(!(I (\[iS.\]llll(:l.ioli. Ih,w 
O,V(H'> (Hie should note tha, t fills dis.iun(: 
l;ion is only l)l'eSeUl; b(~(:aats(~ the \['oaJ, tli'O~i 
.f a,\]l(l g ha>l)l)en 1:o I)o Fir(~s(HIt. Tilt!S(! I(,a 
tures would .eed l;o Im l)res(mt il w(~ wtwe 
enforchl<ej (Jaxpcnl,(H"s \[:7\] lcil, al w(ql i.yl)iug 
r(xluiroti\]oilt ~ whhth ,qa,y's 1.1ial \[(!al:ilr('s I. lial 
a,l:e a.llowed ilillSt 1)o pres,.ml., lllil. Iol.a\[ well 
I.yping is, hi fax:t> incoinl)a.lib\]e ;villi lype 
resolul, ioli~ since I;hore lilil$' w(ql I)o all inli 
llit;(~ seL of tota, lly w(,ll iyl)od I'esolvalil.s of ;1 
l'(;a, Lllr(J st\]'llcttir('~, For (~xa.llipi(~, a.ll illi(lei'.- 
Sl)ocifiod list stl'u('tlir(' couhl be iT(~S()/v0(I 1.o 
;~ list of length (L a. list of h:ngl.h 1, el.c, 
,qhlce I, ota.I well I,yliin g is liOt i'(!quir(!(\[, 
we lm~y i~s well a.ctiwqy un\[il\[ r0(lulid;lnt 
\['0a, tlires, 5 ill this (!Xalli\[)l(!> i\[ t, li(' f ail(l (7 
fo.a, tllrOS ;~l'e reliiovod, we a,lO lell wil, h lh(, 
simple, disjunction {if,/'~}: which is (!quiv- 
a,lent, to l;\]le or(lillaJ'y l,Yl)(' l.(; Thus, iu lliis 
ca, so> \]lO (lisjtulcl, ion a.t all ix rc!(llliro(l 10 (!11" 
force the I"CIL All th',tt is requirc(I is tim 
~qntuil, ively, \[eat, ui'cs arc rodundaui it Ilwir val 
llCS art'. eul,h'cl 5 predictaldc fl'oui ihc approluiaic 
.ross Sl>eCificatim,..%'c GStz \[1)\], (',cr,lemam, \[7\] k,r 
;I. IIlOl;('. \[HXX:iHC forUllllalioii. 
°\[n this casc, il. would also have b(:ml l)~>,~iblc 
to unlill Lhc oi'i<eiuai teal, life Sll'tl<ltllc I,.I.ie I*' 
solviug. /Snforl, unai,e, ly, llmvcvcr, this i~; l.>i ;ihvay~. 
the (:asc, as C;lll |)(! S(!t'II in the \[ollowiug (!Xalll\])lC: 
t{j: +\] :> {C/: +\]} ~ ~'. 
asSUml)tion tha.t t will only be ext(mded 
I)y unil'ying il with a.lmther (t;Oml)a.ct(~d) 
m(mll)(!r o\[' "l)'\]?.Jr,_c,. 
This, h.w(wer, wa.s a. simple ca.se iu 
which a.I1 of the named dis.jun(:tion could 
ho removed. It would not lmve I)('en i)os 
sihle to relnov(' tim fea.tur('s f ~tll(I g if 
thest~ 17,atu\['es had I)oen involved iu re(m- 
tranci(+s of i\[' tlt(,se lim.tures ha.d ha.d t:om- 
i)h+x va.lu('s, lu gt+tlera.I, howover, our eXl)e- 
ri(!ll(:(~ ha,s I)(~(ql that, eV(;l! wil, li very (:()tit 
pl('x type hi(~ra, rchi(~s a.nd |'(m, tur(; SLI'UC- 
l, lll'eS \[()1" liPS(i, very i'ow named (lisjunc- 
lions a, re introdu('e(l. 7 q'hus~ uuilica.1;ion is 
e;(merally uo more (~xp(msive tha.n unifica.- 
li,:)H with unlylmd l(mt.ur(~ sl.fu(:l.ur('s. 
4 CONCLUSIONS 
\% havc~ sh,:Y, vu in this i~al),:~r tha.t the kind 
of consl raints ,:~Xl)r.t~ssihlo Ity api)Vol)rh~,l;o- 
r.~ss c~mdit.ions call he imlflemc'.nted iN a 
i.'actical .,.D, sle\]n e,ul)loyinK typ,M featu r,:'~ 
st.ru(:t.uf(,s and utdlica.Lion a.s I.he I:,ritna.ry 
Ol)(U'a,t, ic:,n on t(>;t,l, ur<+ ,'-;t, ruct, ure~. Ilut what. 
Of IIlOl'(' COIII\[)I(~N l;yp(~ CC'IIH|,F.~LilI|,,q it~v'.)l',.' 
h~y; r(~enl;ram:ies': \[ntro(IL~ciug reeJH.ra.ncies 
illl. ,::<rest ralid.s allows E.' the F,O~sihillty of 
d(~liNiu/,, recursivc l.yl),:~s ~ such a.s the (leli 
nitkm of append in \[I\]. (;lea\['ly the re 
~olv;-~nl.~, o\[ such a. recursiv(~ l.yl)(', could Not 
I)(~ l,reCOmlfiled a.s r,.~quiI'oxl in Troll. 
Oue might, uew'rtholoss, considm' a l- 
\[OWil\]l\[ f('(Hl(, f a, ll('y- ('OIls t f a hI| S oll lloll- 
recursiv(qy defiltcd l.ypcs. A \])ro/)leul still 
arises; nantcly, il lhe l'eSo\[va.itts of a Frail, till't1 
.qll'tlCI411"(~ ill(:ludcd sonic with a pa.rticu 
lar r(~onll'all(:y a.nd s()Tn(~ \viLh(',ul, then the 
(:,.)mliti()ll iliad, a.II resc)lva.uts ha.v(~ th,:~ same 
shal)(~ would m)lon~e\[' hold. ()ue v.,ottkl 
l.her(q'or,.~ no(~(l i.o eml)loy a moue COml)l(,x 
vorsion .r ,a.med (lis.it, f,t:tio, (Ill\], \[12\], 
tit)I). It. ig (i,.L(~sti,.malfl(~ wh('thef such a.d 
ditional (:()mpl(~xit.y would I)e justified to 
'Our CXl)ericl~(:c is derived l,'imarily flora test- 
i.I" Ihc 'l'loll system (m a tat, her lar<e,e e, ramul;G 
for (',(!l>lll;lll imfiial vcrh I>lHases, which was wiit- 
t('n I)y I'hhard Ilillrichs a.d Tsum:ko Na, kazawa 
aud iinl)lclncut,cd by I)clmar McuH_:J's. 
959 
handle this limited class of reentrancy- 
constraints. 
It seems then, that the class of con- 
straints that can be expressed by appro- 
priateness conditions corresponds closely 
to the class of constraints that can be effi- 
ciently preeompiled. We take this as a jus- 
tification for appropriateness formalisms 
in general. It makes sense to ~d)straet out 
the efficiently processable constraints and 
then allow another mechalfiSm, such as at- 
tachments of definite clauses, to express 
more complex constraints. 
References 
\[1\] l\[asmn Ait-Kaci. A New Model of 
Computation Based on a Calculus of 
Type Subsum, ption. Phi) thesis, Uni- 
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\[2\] Bob Carpenter. the Logic of "\]!qped 
l;~ature ,5'tructurcs. (~ambridge q>acts 
in Theoretical Computer Science :{2. 
Cambridge University Press, 1992. 
\[3\] Bob Carpenter. AI,E The Attribute 
Logic Engine, U.ser'.s Guide, 1993. 
\[4\] Ann Copestake, Antonio Saniilippo, 
Ted Briscoe, and Valeria De Paiwl.. 
The ACQUILEX IA{B: An introduc- 
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Inheritance, Defaults, and the Lea:i- 
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t993. 
\[5\] Jochen Darre and Andrea.s Eisele. 
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